One interesting note in the article concerning dubious mathematics in
this century:
History has also shown the dangers of too speculative a style. Early
in this century, Jaffe and Quinn recall, the so-called Italian school
of algebraic geometry "collapsed after a decade of brilliant
speculation" when it becaume apparent that its fundamental assumptions
had never been properly proved. Later mathematicians, unsure of the
field's foundations, avoided it.
I mention this article to the qed mailing list mainly because of the
following very anti-qed remark. Horgan quotes William Thurston of
Berkeley as saying "The idea that mathematics reduces to a set of
formal proofs is itself a shaky idea. In practice, mathematicians
prove theorems in a social context. It think that mathematics that is
highly formalized is more likely to be wrong" than mathematics that is
intuitive.
Bob